Issue: Volume 6, Number 11
Date: November 2006
From: Mark J. Anderson, Stat-Ease, Inc., "Statistics Made Easy" ™ Blog

Dear Experimenter,

Here's another set of frequently asked questions (FAQs) about doing design of experiments (DOE), plus alerts to timely information and free software updates. If you missed the previous DOE FAQ Alert, please click on the links at the bottom of this page. If you have a question that needs answering, click the Search tab and enter the key words. This finds not only answers from previous Alerts, but also other documents posted to the Stat-Ease web site.

Feel free to forward this newsletter to your colleagues. They can subscribe by going to http://www.statease.com/doealertreg.html. If this newsletter prompts you to ask your own questions about DOE, please address them via mail to:StatHelp@StatEase.com.

For an assortment of appetizers to get this Alert off to a good start, see these new blogs at http://statsmadeeasy.net:
— "Drinking twice as much reduces heart attack by factor of three?"
— "Sound from Sand: Rock Music?"
— "Stonehenge blocks demonstrably moved by man — not magic"
— "Lost arts — slide rules and cursive writing"
— "Minnesota Twins beat the statistical odds once again"

Yesterday the citizens of our United States exhibited their mercurial mood by voting for a transit in their political landscape from the right to the left. Today they can see the planet Mercury transit the sun. This happens only about every decade. For an astronomer's eye view (Kitt Peak, Arizona), see the webcast from 11 am to 4 pm PST by San Francisco's Exploratorium at http://www.exploratorium.edu/transit/. I expect that they will save the record of this astronomical event if you miss Mercury actually in transit this time around.

Topics in the body text of this DOE FAQ Alert are headlined below (the "Expert" ones, if any, delve into statistical details).

1. Faq: Why effects plot may change depending on chosen model
2. Info Alert: Poking fun poetically at DOE and statisticians
3. Events alert: Do you seek a speaker?
4. Workshop alert: Last chance for "Experiment Design Made Easy"

PS. Quote for the month: A compelling call for scientists and engineers to learn statistics. (See actual quote at the end of this newsletter.)

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1. FAQ: Why effects plot may change depending on chosen model

-----Original Question-----
From: Ireland
"When looking for the most significant factor in an experiment, I discovered a strange phenomena in your new Design-Expert® software version 7 ("DX7"). Here’s the situation:
1. I designed a two-level factorial and entered my data.
2. I went to the analysis branch and for each response I clicked the effects button to produce the half-normal plot. A somewhat mysterious warning popped up about things being 'not orthogonal.'
3. I then selected the largest effects (furthest to the right off the lineup of trivial near-zero points), and clicked ahead to the ANOVA to see the probability (p-value) that this chosen model was significant.
4. For some responses, if I click back on to the half normal plot, it changes — some selected effects move to a different place on the graph, in some cases near enough to zero that they no longer appear to be significant! Any idea what is happening here?"

Answer:
Evidently your design is not orthogonal, thus the model coefficients are correlated. This happens by design for DX7's new minimum-run options for resolutions IV (main effect screening) and V (looking for interactions).* Another possibility, one that occurs all too often, is that some of your responses went missing or you chose to ignore them.

In any case, you can assess orthogonality via Design-Expert's powerful design evaluation tool by observing the variance inflation factors (VIFs) of the model coefficients. If any VIFs exceed 1, your design is not orthogonal. (Be careful here: If any given response column contains missing or ignored values, evaluate it alone via the new pull-down option in DX7 to specify a single response.)

Do not worry about forgetting to do the evaluation, because when you first click the Effects button, version 7 of Design-Expert (or Design-Ease® V7) warns you that "This design is not orthogonal"
and it advises that you "Click 'Recalculate' to see how the coefficients change depending on the other model terms."

You will find the Recalculate button at the bottom of the floating Effects Tool. I advise that you press this button whenever you choose effects. It may make no difference. However, in a non-orthogonal design the size of the effects are dependent upon which others you choose first. Based on your chosen model, the button causes Design-Expert to recalculate the effects and synchronize them with the analysis of variance, which you create by clicking the next button in the sequence of analysis: "ANOVA."

If you then go back to the half-normal (or Pareto) plot and pick more effects, some of those chosen previously may fall back into the pack of trivial many, near zero. I realize that this analogy is a stretch, but this changing situation reminds me of my childhood days when we would get a group of boys together for a game, choose two captains and let them pick players. Sometimes a really good player would saunter in after sides were chosen, and then one hapless boy would be kicked off a team to make room for the star. In other words, the individual term that stood out initially, falls back into the pack after one that is better steps forward.

It is good that you emailed your DX data file to our consulting staff at StatHelp@StatEase.com so they could try modeling your key responses. Stat-Ease prides itself on providing free help like this. We can draw upon our expertise on DOE to provide a valuable second opinion on design or analysis of a client's experiment. It never hurts to email or call Stat-Ease for statistical help!

"Thanks for your quick answers. A good technical support is one of the decisive things that I look for when choosing software."
— An Italian professor's emailed compliment received today (11/8/06) by Stat-Easae "StatHelp." Consultant Shari Kraber provided him with timely advice on how to design an experiment on rheological behavior of a suspension.

(Learn more about factorial model-building by attending the three-day computer-intensive workshop "Experiment Design Made Easy." See http://www.statease.com/clas_edme.html for a description of this class and then link from this page to the course outline and schedule. Then, if you like, enroll online.)

*See http://www.statease.com/soft_abs.html for details and link from there to free 45-day fully-functional trials of version 7 of Design-Expert software.

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2. Info alert: Poking fun poetically at DOE and statisticians

Our UK associate Alan Collins (see him pictured and introduced at http://www.statease.com/acollins.html) dredged up an old, but still good as gold, poem on DOE titled "Hiawatha Designs an Experiment."* It is a bit too long to re-print here, but you can read it at http://www.math.utah.edu/~cherk/hiawatha.html. If you are in a mood for geeky humor collected by Andrej and Elena Cherkaev, mathematics professors at the University of Utah, click the "back to math jokes" link at the end of this devilishly funny poem on DOE.

*Attributed to various authors in numerous reprints on the internet, but so far as I can tell, it was written by British statistician Maurice Kendall who in his prime produced double the number of random digits, over one hundred thousand, than ever before. Before doing this, he developed a four-test gauntlet that defined whether a series of numbers really are random. For more on Maurice, see http://en.wikipedia.org/wiki/Maurice_Kendall.

PS. Here's a shorter poem I found on the internet:

THE MAGIC OF STATISTICS

The statistician spends his days,
In figuring out the many ways,
In which a standard error can,
Enclose by bars the average man.
And having thus imprisoned him,
Perhaps at some researcher's whim,
Can with the same chicanery,
Enlarge the bars and set him free.
Or better yet, within the sample,
Locate some points with girth so ample,
That if by "choice" they were discarded,
Man and hypothesis are safeguarded.

Joe Mole

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3. Event alert: Do you seek a speaker?

Do you need a speaker on DOE for a learning session within your company or technical society at regional or national levels? If so, contact me. It may not cost you anything if Stat-Ease has a consultant close by. However, for presentations involving travel, we appreciate reimbursements for airfare, hotel and meals — expenses only. In any case, it never hurts to ask Stat-Ease for a speaker on this topic — we are at the foremost ranks of practical expertise on design of experiments for process and product improvement. Contact me at Mark@StatEase.com if you have an event coming up with an open slot for a presentation.

PC. Click http://www.statease.com/events.html for a list of appearances by Stat-Ease professionals. We hope to see you sometime in the near future!

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4. Work alert: Last chance for "Experiment Design Made Easy"

The last public presentation of "Experiment Design Made Easy" for 2006 will be held on December 5-7 at the Stat-Ease computer training center in Minneapolis. See http://www.statease.com/clas_edme.html for further information and link from there to register online. See http://www.statease.com/clas_pub.html for schedule and site information on all Stat-Ease workshops open to the public. To enroll, click the "register online" link on our web site or call Stat-Ease at 612.378.9449. If spots remain available, bring along several colleagues and take advantage of quantity discounts in tuition, or consider bringing in an expert from Stat-Ease to teach a private class at your site.* Call us to get a quote.

*Believe it or not, it only takes a class of 4 students to make it economical for Stat-Ease to come and teach at your site versus sending them out to one of our public presentations. The economics are detailed in the July 2006 issue of the Stat-Teaser newsletter at http://www.statease.com/news/news0608.pdf.

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I hope you learned something from this issue. Address your general questions and comments to me at: Mark@StatEase.com.

Sincerely,

Mark

Mark J. Anderson, PE, CQE
Principal, Stat-Ease, Inc. (http://www.statease.com)
2021 East Hennepin Avenue, Suite 480
Minneapolis, Minnesota 55413 USA

PS. Quote for the month — A compelling call for scientists and engineers to learn statistics:
"The long-range contribution of statistics depends not so much upon getting a lot of highly trained statisticians into the industry as it does on creating a statistically minded generation of physicists, chemists, engineers, and others who will in any way have a hand in developing and directing the production processes of tomorrow."
— Walter A. Shewhart, the "Father of statistical quality control" according to the American Society of Quality (ASQ) — see http://www.asq.org/about-asq/who-we-are/bio_shewhart.html.
 
Trademarks: Design-Ease, Design-Expert and Stat-Ease are registered trademarks of Stat-Ease, Inc.

Acknowledgements to contributors:
—Students of Stat-Ease training and users of Stat-Ease software
—Stat-Ease consultants Pat Whitcomb, Shari Kraber and Wayne Adams (see http://www.statease.com/consult.html for resumes)
—Statistical advisor to Stat-Ease: Dr. Gary Oehlert (http://www.statease.com/garyoehl.html)
—Stat-Ease programmers, especially Tryg Helseth and Neal Vaughn (http://www.statease.com/pgmstaff.html)
—Heidi Hansel, Stat-Ease marketing director, and all the remaining staff

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Interested in previous FAQ DOE Alert e-mail newsletters?
To view a past issue, choose it below.

#1 Mar 01, #2 Apr 01, #3 May 01, #4 Jun 01, #5 Jul 01 , #6 Aug 01, #7 Sep 01, #8 Oct 01, #9 Nov 01, #10 Dec 01, #2-1 Jan 02, #2-2 Feb 02, #2-3 Mar 02, #2-4 Apr 02, #2-5 May 02, #2-6 Jun 02, #2-7 Jul 02, #2-8 Aug 02, #2-9 Sep 02, #2-10 Oct 02, #2-11 Nov 02, #2-12 Dec 02, #3-1 Jan 03, #3-2 Feb 03, #3-3 Mar 03, #3-4 Apr 03, #3-5 May 03, #3-6 Jun 03, #3-7 Jul 03, #3-8 Aug 03, #3-9 Sep 03 #3-10 Oct 03, #3-11 Nov 03, #3-12 Dec 03, #4-1 Jan 04, #4-2 Feb 04, #4-3 Mar 04, #4-4 Apr 04, #4-5 May 04, #4-6 Jun 04, #4-7 Jul 04, #4-8 Aug 04, #4-9 Sep 04, #4-10 Oct 04, #4-11 Nov 04, #4-12 Dec 04, #5-1 Jan 05, #5-2 Feb 05, #5-3 Mar 05, #5-4 Apr 05, #5-5 May 05, #5-6 Jun 05, #5-7 Jul 05, #5-8 Aug 05, #5-9 Sep 05, #5-10 Oct 05, #5-11 Nov 05, #5-12 Dec 05, #6-01 Jan 06, #6-02 Feb 06, #6-03 Mar 06, #6-4 Apr 06, #6-5 May 06, #6-6 Jun 06, #6-7 Jul 06, #6-8 Aug 06, #6-9 Sep 06, #6-10 Oct 06, #6-11 Nov 06(see above)

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